What do the following two equations represent? $4x-5y = -3$ $5x+4y = 2$
Solution: Putting the first equation in $y = mx + b$ form gives: $4x-5y = -3$ $-5y = -4x-3$ $y = \dfrac{4}{5}x + \dfrac{3}{5}$ Putting the second equation in $y = mx + b$ form gives: $5x+4y = 2$ $4y = -5x+2$ $y = -\dfrac{5}{4}x + \dfrac{1}{2}$ The slopes are negative inverses of each other, so the lines are perpendicular.